On a coordinate plane, create LMN where LN is a vertical line segment and MN is a horizontal line segment.
b. Then create QR parallel to LM such that point Q is on LN and point R is on MN.
c. Label points L, M, N, Q, and R with their coordinates.
d. Use the slope formula to confirm that QR is parallel to LM.
To create LMN where LN is a vertical line segment and MN is a horizontal line segment, we can choose any suitable points for L, M, and N.
Let's say L coordinates are (-3, 0), M coordinates are (0, 0), and N coordinates are (0, 4).
b. To create QR parallel to LM, we need to maintain the same vertical component of LN while changing the horizontal component. We can choose any suitable horizontal value for R, but it must have the same vertical component as N.
For example, let's choose R coordinates as (4, 4) since it has the same vertical component as N.
c. Label points L, M, N, Q, and R with their coordinates:
L (-3, 0)
M (0, 0)
N (0, 4)
Q (-3, 4)
R (4, 4)
d. To confirm that QR is parallel to LM using the slope formula, we need to find the slopes of both line segments.
Slope of LM:
m(LM) = (y₂ - y₁) / (x₂ - x₁)
= (0 - 0) / (0 - (-3))
= 0/3
= 0
Slope of QR:
m(QR) = (y₂ - y₁) / (x₂ - x₁)
= (4 - 4) / (4 - (-3))
= 0 / 7
= 0
Since the slopes of LM and QR are both 0, they are parallel to each other.